Aswath Damodaran INVESTMENT VALUATION: SECOND

5the firms being compared. The second step is to be aware of the cross sectionaldistribution of the multiple, not only across firms in the sector being analyzed but alsoacross the entire market. The third step is to analyze the multiple and understand notonly what fundamentals determine the multiple but also how changes in thesefundamentals translate into changes in the multiple. The final step is finding the rightfirms to use for comparison and controlling for differences that may persist across thesefirms.A. Definitional TestsEven the simplest multiples can be defined differently by different analysts.Consider, for instance, the price earnings ratio (PE). Most analysts define it to be themarket price divided by the earnings per share but that is where the consensus ends.There are a number of variants on the PE ratio. While the current price is conventionallyused in the numerator, there are some analysts who use the average price over the last sixmonths or a year. The earnings per share in the denominator can be the earnings per sharefrom the most recent financial year (yielding the current PE), the last four quarters ofearnings (yielding the trailing PE) and expected earnings per share in the next financialyear (resulting in a forward PE). In addition, earnings per share can be computed basedupon primary shares outstanding or fully diluted shares and can include or excludeextraordinary items. Figure 17.1 provides some of the PE ratios for Cisco in 1999 usingvariants of these measures.

6Figure 17.1: Estimate of Cisco's PE ingForwardDiluted beforeExtraordinaryDiluted afterExtraordinaryNot only can these variants on earnings yield vastly different values for the priceearnings ratio, but the one that gets used by analysts depends upon their biases. Forinstance, in periods of rising earnings, the forward PE yields consistently lower valuesthan the trailing PE, which, in turn, is lower than the current PE. A bullish analyst willtend to use the forward PE to make the case that the stock is trading at a low multiple ofearnings, while a bearish analyst will focus on the current PE to make the case that themultiple is too high. The first step when discussing a valuation based upon a multiple isto ensure that everyone in the discussion is using the same definition for that multiple.ConsistencyEvery multiple has a numerator and a denominator. The numerator can be either anequity value (such as market price or value of equity) or a firm value (such as enterprisevalue, which is the sum of the values of debt and equity, net of cash). The denominatorcan be an equity measure (such as earnings, net income or book value of equity) or a firmmeasure (such as operating income, EBITDA or book value of capital).

7One of the key tests to run on a multiple is to examine whether the numerator anddenominator are defined consistently. If the numerator for a multiple is an equity value,then the denominator should be an equity value as well. If the numerator is a firm value,then the denominator should be a firm value as well. To illustrate, the price earnings ratiois a consistently defined multiple, since the numerator is the price per share (which is anequity value) and the denominator is earnings per share (which is also an equity value). Sois the Enterprise value to EBITDA multiple, since the numerator and denominator areboth firm value measures.Are there any multiples in use that are inconsistently defined? Consider the priceto EBITDA multiple, a multiple that has acquired adherents in the last few years amonganalysts. The numerator in this multiple is an equity value and the denominator is ameasure of earnings to the firm. The analysts who use this multiple will probably arguethat the inconsistency does not matter since the multiple is computed the same way forall of the comparable firms; but they would be wrong. If some firms on the list have nodebt and others carry significant amounts of debt, the latter will look cheap on a price toEBITDA basis, when in fact they might be over or correctly priced.UniformityIn relative valuation, the multiple is computed for all of the firms in a group andthen compared across these firms to make judgments on which firms are over priced andwhich are under priced. For this comparison to have any merit, the multiple has to bedefined uniformly across all of the firms in the group. Thus, if the trailing PE is used forone firm, it has to be used for all of the others as well. In fact, one of the problems withusing the current PE to compare firms in a group is that different firms can have differentfiscal-year ends. This can lead to some firms having their prices divided by earnings fromJuly 1999 to June 2000, with other firms having their prices divided by earnings fromJanuary 1999 to December 1999. While the differences can be minor in mature sectors,where earnings do not make quantum jumps over six months, they can be large in highgrowth sectors.With both earnings and book value measures, there is another component to beconcerned about and that is the accounting standards used to estimate earnings and book

8values. Differences in accounting standards can result in very different earnings and bookvalue numbers for similar firms. This makes comparisons of multiples across firms indifferent markets, with different accounting standards, very difficult. Even within theUnited States, the fact that some firms use different accounting rules (on depreciation andexpensing) for reporting purposes and tax purposes and others do not can throw offcomparisons of earnings multiples1.B. Descriptional TestsWhen using a multiple, it is always useful to have a sense of what a high value, a lowvalue or a typical value for that multiple is in the market. In other words, knowing thedistributional characteristics of a multiple is a key part of using that multiple to identifyunder or over valued firms. In addition, you need to understand the effects of outliers onaverages and unearth any biases in these estimates, introduced in the process of estimatingmultiples.Distributional CharacteristicsMany analysts who use multiples have a sector focus and have a good sense ofhow different firms in their sector rank on specific multiples. What is often lacking,however, is a sense of how the multiple is distributed across the entire market. Why, youmight ask, should a software analyst care about price earnings ratios of utility stocks?Because both software and utility stocks are competing for the same investment dollar,they have to, in a sense, play by the same rules. Furthermore, an awareness of howmultiples vary across sectors can be very useful in detecting when the sector you areanalyzing is over or under valued.What are the distributional characteristics that matter? The standard statistics –the average and standard deviation – are where you should start, but they represent thebeginning of the exploration. The fact that multiples such as the price earnings ratio cannever be less than zero and are unconstrained in terms of a maximum results indistributions for these multiples that are skewed towards the positive values.1Firms that adopt different rules for reporting and tax purposes generally report higher earnings to theirstockholders than they do to the tax authorities. When they are compared on a price earnings basis to firms

9Consequently, the average values for these multiples will be higher than median values2,and the latter are much more representative of the typical firm in the group. While themaximum and minimum values are usually of limited use, the percentile values (10thpercentile, 25 th percentile, 75th percentile, 90th percentile, etc.) can be useful in judgingwhat a high or low value for the multiple in the group is.Outliers and AveragesAs noted earlier, multiples are unconstrained on the upper end and firms can haveprice earnings ratios of 500 or 2000 or even 10000. This can occur not only because ofhigh stock prices but also because earnings at firms can sometime drop to a few cents.These outliers will result in averages that are not representative of the sample. In mostcases, services that compute and report average values for multiples either throw outthese outliers when computing the averages or constrain the multiples to be less than orequal to a fixed number. For instance, any firm that has a price earnings ratio greater than500 may be given a price earnings ratio of 500.When using averages obtained from a service, it is important that you know howthe service dealt with outliers in computing the averages. In fact, the sensitivity of theestimated average to outliers is another reason for looking at the median values formultiples.Biases in Estimating MultiplesWith every multiple, there are firms for which the multiple cannot be computed.Consider again the price-earnings ratio. When the earnings per share are negative, the priceearnings ratio for a firm is not meaningful and is usually not reported. When looking at theaverage price earnings ratio across a group of firms, the firms with negative earnings willall drop out of the sample because the price earnings ratio cannot be computed. Whyshould this matter when the sample is large? The fact that the firms that are taken out ofthe sample are the firms losing money creates a bias in the selection process. In fact, thethat do not maintain different reporting and tax books, they will look cheaper (lower PE).2 With the median, half of all firms in the group fall below this value and half lie above.

10average PE ratio for the group will be biased upwards because of the elimination of thesefirms.There are three solutions to this problem. The first is to be aware of the bias andbuild it into the analysis. In practical terms, this will mean adjusting the average PE downto reflect the elimination of the money-losing firms. The second is to aggregate the marketvalue of equity and net income (or loss) for all of the firms in the group, including themoney-losing ones, and compute the price earnings ratio using the aggregated values.Figure 17.2 summarizes the average PE ratio, the median PE ratio and the PE ratio basedupon aggregated earnings for specialty retailers.Figure 17.2: PE Ratio for Specialty Retailers25.0020.0015.0010.005.000.00Aerage PE ratioMedian PE ratioPE ratio based upon aggregateNote that the median PE ratio is much lower than the average than the PE ratio.Furthermore, the PE ratio based upon the aggregate values of market value of equity andnet income is lower than the average across firms where PE ratios could be computed. Thethird choice is to use a multiple that can be computed for all of the firms in the group. Theinverse of the price earning ratio, which is called the earnings yield, can be computed forall firms, including those losing money.

11C. Analytical TestsIn discussing why analysts were so fond of using multiples, it was argued that relativevaluations require fewer assumptions than discounted cash flow valuations. While this istechnically true, it is only so on the surface. In reality, you make just as manyassumptions when you do a relative valuation as you make in a discounted cash flowvaluation. The difference is that the assumptions in a relative valuation are implicit andunstated, whereas those in discounted cash flow valuation are explicit and stated. The twoprimary questions that you need to answer before using a multiple are: What are thefundamentals that determine at what multiple a firm should trade? How do changes in thefundamentals affect the multiple?DeterminantsIn the introduction to discounted cash flow valuation, you observed that the valueof a firm is a function of three variables – it capacity to generate cash flows, its expectedgrowth in these cash flows and the uncertainty associated with these cash flows. Everymultiple, whether it is of earnings, revenues or book value, is a function of the same threevariables – risk, growth and cash flow generating potential. Intuitively, then, firms withhigher growth rates, less risk and greater cash flow generating potential should trade athigher multiples than firms with lower growth, higher risk and less cash flow potential.The specific measures of growth, risk and cash flow generating potential that areused will vary from multiple to multiple. To look under the hood, so to speak, of equityand firm value multiples, you can go back to fairly simple discounted cash flow modelsfor equity and firm value and use them to derive the multiples.In the simplest discounted cash flow model for equity, which is a stable growthdividend discount model, the value of equity is:Value of Equity P0 DPS1ke gnwhere DPS1 is the expected dividend in the next year, ke is the cost of equity and gn is theexpected stable growth rate. Dividing both sides by the earnings, you obtain thediscounted cash flow equation specifying the PE ratio for a stable growth firm.

12P0Payout Ratio*(1 gn ) PE EPS0k e -g nDividing both sides by the book value of equity, you can estimate the price/book valueratio for a stable growth firm.P0ROE*Payout Ratio*(1 g n ) PBV BV0k e -gnwhere ROE is the return on equity. Dividing by the Sales per share, the price/sales ratiofor a stable growth firm can be estimated as a function of its profit margin, payout ratio,risk and expected growth.P0Profit Margin*Payout Ratio*(1 gn ) PS Sales0k -genYou can do a similar analysis to derive the firm value multiples. The value of afirm in stable growth can be written as:Value of Firm V0 FCFF1kc g nDividing both sides by the expected free cash flow to the firm yields the Value/FCFFmultiple for a stable growth firm.V01 FCFF1 k c gnSince the free cash flow the firm is the after-tax operating income netted againstthe net capital expenditures and working capital needs of the firm, the multiples of EBIT,after-tax EBIT and EBITDA can also be estimated similarly.The point of this analysis is not to suggest that you go back to using discountedcash flow valuation, but to understand the variables that may cause these multiples tovary across firms in the same sector. If you ignore these variables, you might concludethat a stock with a PE of 8 is cheaper than one with a PE of 12 when the true reason maybe that the latter has higher expected growth or you might decide that a stock with a P/BV

13ratio of 0.7 is cheaper than one with a P/BV ratio of 1.5 when the true reason may be thatthe latter has a much higher return on equity.RelationshipKnowing the fundamentals that determine a multiple is a useful first step, butunderstanding how the multiple changes as the fundamentals change is just as critical tousing the multiple. To illustrate, knowing that higher growth firms have higher PE ratios isnot a sufficient insight if you are called upon to analyze whether a firm with a growth ratethat is twice as high as the average growth rate for the sector should have a PE ratio that is1.5 times or 1.8 times or two times the average price earnings ratio for the sector. Tomake this judgment, you need to know how the PE ratio changes as the growth ratechanges.A surprisingly large number of analyses are based upon the assumption that thereis a linear relationship between multiples and fundamentals. For instance, the PEG ratio,which is the ratio of the PE to the expected growth rate of a firm and widely used toanalyze high growth firms, implicitly assumes that PE ratios and expected growth ratesare linearly related.One of the advantages of deriving the multiples from a discounted cash flowmodel, as was done in the last section, is that you can analyze the relationship betweeneach fundamental variable and the multiple by keeping everything else constant andchanging the value of that variable. When you do this, you will find that there are veryfew linear relationships in valuation.Companion VariableWhile the variables that determine a multiple can be extracted from a discountedcash flow model and the relationship between each variable and the multiple can bedeveloped by holding all else constant and asking what-if questions, there is one variablethat dominates when it comes to explaining each multiple. This variable, which is calledthe companion variable, can usually be identified by looking at how multiples are differentacross firms in a sector or across the entire market. In the next two chapters, thecompanion variables for the most widely used multiples from the price earnings ratio tothe value to sales multiples are identified and then used in analysis.

14D. Application TestsWhen multiples are used, they tend to be used in conjunction with comparablefirms to determine the value of a firm or its equity. But what is a comparable firm? Whilethe conventional practice is to look at firms within the same industry or business ascomparable firms, this is not necessarily always the correct or the best way of identifyingthese firms. In addition, no matter how carefully you choose comparable firms,differences will remain between the firm you are valuing and the comparable firms.Figuring out how to control for these differences is a significant part of relative valuation.What is a comparable firm?A comparable firm is one with cash flows, growth potential, and risk similar to thefirm being valued. It would be ideal if you could value a firm by looking at how an exactlyidentical firm - in terms of risk, growth and cash flows - is priced. Nowhere in thisdefinition is there a component that relates to the industry or sector to which a firmbelongs. Thus, a telecommunications firm can be compared to a software firm, if the twoare identical in terms of cash flows, growth and risk. In most analyses, however, analystsdefine comparable firms to be other firms in the firm’s business or businesses. If there areenough firms in the industry to allow for it, this list is pruned further using other criteria;for instance, only firms of similar size may be considered. The implicit assumption beingmade here is that firms in the same sector have similar risk, growth, and cash flow profilesand therefore can be compared with much more legitimacy.This approach becomes more difficult to apply when there are relatively fewfirms in a sector. In most markets outside the United States, the number of publiclytraded firms in a particular sector, especially if it is defined narrowly, is small. It is alsodifficult to define firms in the same sector as comparable firms if differences in risk,growth and cash flow profiles across firms within a sector are large. Thus, there may behundreds of computer software companies listed in the United States, but the differencesacross these firms are also large. The tradeoff is therefore a simple one. Defining anindustry more broadly increases the number of comparable f

Aswath Damodaran INVESTMENT VALUATION: SECOND EDITION Chapter 1: Introduction to Valuation 3 Chapter 2: Approaches to Valuation 16 Chapter 3: Understanding Financial Statements 37 Chapter 4: The Basics of Risk 81 Chapter 5: Option Pricing Theory and Models 121 Chapter 6: Market Efficiency: Theory and Models 152 .